Is there an alternative to dark matter? I've been reading about dark matter. I understood that its existence is inferred by the discrepancy between the gravity exerted by a galaxy (total mass) and the movement of the stars that compose it. 
In other words, the outer stars would not behave as they do if the total mass of the system was not much higher than can be seen. 
I wondered if there are other possible explanations for this phenomenon instead of dark matter.
 A: The evidence for dark matter is extremely compelling provided that Einstein's theory of relativity is assumed. To get out of dark matter means dropping that assumption (or that we've SERIOUSLY botched some observations). Some people study alternate theories of gravity. The two alternate theories (or classes of theories? keywords?) I hear most about are f(R) gravity and MOND: MOdified Newtonian Dynamics.
A: While Milgrom's MOND theory and its relativistic generalization by Jacob Bekenstein called TeVeS provides one gravity modification approach which is the earliest and most famous, it is not the only one. A variety of proposals have been seriously considered in the last six years alone:
John W. Moffat has several others similar in concept such as MOG. There are f(R) and f(R,T) theories which have additional terms which are functions of the Ricci tensor and torsion scalar respectively. Non-local gravity formulations have been proposed to address dark matter phenomena. Then there are concepts like that of Alexandre Deur who reconsiders how the self-interaction of the graviton should be handled in quantum gravity (explored previously as early as 1981), and Lee Smolin who considers quantum gravity effects that could appear to be dark matter in loop quantum gravity approaches. Erik Verlinde's Emergent Gravity concept didn't set out to be a gravity modification approach but some versions of it provide an alternative to dark matter. Some running gravitational coupling constant solutions (also here) could also replace dark matter, possibly in connection with an asymptotically safe gravity scenario. Horndeski gravity was invented as an alternative dark energy realization but can be a dark matter alternative as well, as can be a generalisation of Brans-Dicke theory. A massive scalar graviton and tensor massive gravity (also here) have also been considered as an alternatives. Lubos Motl has advanced a variant called holographic modified dynamics. 
Wave dark matter is strictly speaking a dark matter particle theory, but has some characteristics usually found in gravity modification theories.
